Question
Solve the equation.
StartFraction x Over 3 EndFraction plus 2 equals StartFraction x Over 3 EndFraction
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
xequals
enter your response here
B.
The solution is all real numbers.
C.
There is no solution.
StartFraction x Over 3 EndFraction plus 2 equals StartFraction x Over 3 EndFraction
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
xequals
enter your response here
B.
The solution is all real numbers.
C.
There is no solution.
Answers
GPT-4o mini
To solve the equation
\[
\frac{x}{3} + 2 = \frac{x}{3},
\]
we can start by isolating the variable \( x \).
1. **Subtract \(\frac{x}{3}\) from both sides:**
\[
2 = \frac{x}{3} - \frac{x}{3} + \frac{x}{3},
\]
which simplifies to:
\[
2 = 0.
\]
2. Since the statement \(2 = 0\) is false, it indicates that our original equation has no solution.
Thus, the correct answer is:
**C. There is no solution.**
\[
\frac{x}{3} + 2 = \frac{x}{3},
\]
we can start by isolating the variable \( x \).
1. **Subtract \(\frac{x}{3}\) from both sides:**
\[
2 = \frac{x}{3} - \frac{x}{3} + \frac{x}{3},
\]
which simplifies to:
\[
2 = 0.
\]
2. Since the statement \(2 = 0\) is false, it indicates that our original equation has no solution.
Thus, the correct answer is:
**C. There is no solution.**